Gate complexity using Dynamic Programming

TL;DR

This paper explores how dynamic programming from control theory can optimize quantum gate synthesis, demonstrating its effectiveness through simulations on SU(2) systems to analyze gate complexity.

Contribution

It introduces a novel application of dynamic programming for quantum circuit synthesis, bridging control theory and quantum computing.

Findings

Dynamic programming can optimize quantum gate synthesis.

Simulation results show reduced gate complexity.

Sample paths illustrate the synthesis process.

Abstract

The relationship between efficient quantum gate synthesis and control theory has been a topic of interest in the quantum control literature. Motivated by this work, we describe in the present article how the dynamic programming technique from optimal control may be used for the optimal synthesis of quantum circuits. We demonstrate simulation results on an example system on SU(2), to obtain plots related to the gate complexity and sample paths for different logic gates.